Quasi-nonexpansive Selections and Convergence Theorems for Multivalued Nonexpansive Mappings in Banach Spaces

Authors

Keywords:

multivalued nonexpansive mapping, quasi-nonexpansive, uniformly convex, selection, fixed point

Abstract

In this work, we investigate selections of multivalued mappings. We also prove that a multivalued nonexpansive mapping with endpoint property in a Banach space has a quasi-nonexpansive selection. We apply our results to prove a weak convergence theorem for a common fixed point of a single-valued and a multivalued mapping in uniformly convex Banach spaces.

Author Biographies

Sunisa Somsit, Department of Mathematics, Faculty of Science, Chiang Mai University

Master’s Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Annop Kaewkhao, Department of Mathematics, Faculty of Science, Burupha University

Assistant Professor at Department of Mathematics, Faculty of Science, Burupha University, Chonburi 20131, Thailand

Attapol Kaewkhao, Department of Mathematics, Faculty of Science, Chiang Mai University

Associate Professor at Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty
of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Bancha Panyanak, Department of Mathematics, Faculty of Science, Chiang Mai University

Associate Professor at  Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Warunun Inthakon, Department of Mathematics, Faculty of Science, Chiang Mai University

Associate Professor at Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty
of Science, Chiang Mai University, Chiang Mai 50200, Thailand

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Published

2022-10-01

How to Cite

Somsit, S., Kaewkhao, A., Kaewkhao, A., Panyanak, B., & Inthakon, W. (2022). Quasi-nonexpansive Selections and Convergence Theorems for Multivalued Nonexpansive Mappings in Banach Spaces. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(2), 131–139. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/81

Issue

Vol. 1 No. 2 (2022): July - December, 2022

Section

Articles

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Copyright (c) 2022 Sunisa Somsit, Annop Kaewkhao, Attapol Kaewkhao, Bancha Panyanak, Warunun Inthakon

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